Passive Vibration Shape Control of Frame Structure by Homology Design.

A formulation of homology design is presented for passive control of a structural shape under dynamic excitations. Prescribed geometrical property in a part of structure is kept both in vibrant state and standstill one by homology design for the purpose to reduce control cost expected for high quality of performance. Time-history analysis is carried out by the Newmark β method to evaluate the error index, which indicates the time-average of the difference from the objective homologous vibration shape. The error index is minimized by iterative renewals using the finite element sensitivity analysis and the Newton's method. The validity of the proposed formulation is demonstrated in a numerical example concerning with planar lattice frame, a square portion of which is kept horizontal even in a vibrant state by homology design.